Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us t...

Integrated information systems provide users with a single unified view to heterogeneous data sources. As the resolution of schema level conflicts and the detection of fuzzy duplicates has been looked at more comprehensively, the problem of resolving data level conflicts still remains. We propose a relational data fusion operator, which fuses tuples representing the same real world entity by re...

This study presents a novel controller of magnetic levitation system by using new neuro-fuzzy structures which called flexible neuro-fuzzy systems. In this type of controller we use sliding mode control with neuro-fuzzy to eliminate the Jacobian of plant. At first, we control magnetic levitation system with Mamdanitype neuro-fuzzy systems and logical-type neuro-fuzzy systems separately and then...

This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system Ev L of fuzzy logic that has evaluated syntax, i.e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of Gödel’s completeness theorem does hold in Ev L. The truth values form...

We introduce a linear analogue of Lauchli's semantics for intuitionistic logic. In fact, our result is a strengthening of L auchli's work to the level of proofs, rather than provability. This is obtained by considering continuous actions of the additive group of integers on a category of topological vector spaces. The semantics, based on functorial polymorphism, consists of dinatural transfor...

We present logic programming style “goal-directed” proof methods for Lukasiewicz logic L that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational P...

Connections between Algebraic Logic and (ordinary) Logic. Algebraic counterpart of model theoretic semantics, algebraic counterpart of proof theory, and their connections. The class Alg(L) of algebras associated to any logic L. Equivalence theorems stating that L has a certain logical property iff Alg(L) has a certain algebraic property. (E.g. L admits a strongly complete Hilbertstyle inference...

in this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. it would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. we give the main properties of the operations defined and prove som...

The subject of the study was hardware implementations of fuzzy controllers as CMOS analog devices on the base of implementation of fuzzy inference rules as multi-valued logic functions using summing amplifiers as building blocks. Earlier a functional completeness of summing amplifier with saturation in an arbitrary-valued logic was proven that gave a theoretical background for analog implementa...